Edge rings satisfying Serre's condition R_1

A combinatorial criterion for the edge ring of a finite connected graph to satisfy Serre's condition R_1 is studied

Two way subtable sum problems and quadratic Groebner bases

Hara, Takemura and Yoshida discuss toric ideals arising from two way subtable sum problems and shows that these toric ideals are generated by quadratic binomials if and only if the subtables are either diagonal or triangular. In the present paper, we show that if the subtables are either diagonal or triangular, then their toric ideals possess quadratic Groebner bases.Comment: 3 page